Reduced-order controllers for the H∞ control problem with unstable invariant zeros

Automatica ◽  
2004 ◽  
Vol 40 (2) ◽  
pp. 319-326 ◽  
Author(s):  
Xin Xin
Keyword(s):  
Control Problem ◽  
Reduced Order

LQG Control for Nonstandard Singularly Perturbed Discrete-Time Systems

2004 ◽  
Vol 126 (4) ◽  
pp. 860-864 ◽  
Author(s):  
Beom-Soo Kim ◽  
Young-Joong Kim ◽  
Myo-Taeg Lim
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Discrete Time ◽  
Singularly Perturbed ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Reduced Order ◽  
Discrete Time Systems ◽  
Time Systems

In this paper we present a control method and a high accuracy solution technique in solving the linear quadratic Gaussian problems for nonstandard singularly perturbed discrete time systems. The methodology that exists in the literature for the solution of the standard singularly perturbed discrete time linear quadratic Gaussian optimal control problem cannot be extended to the corresponding nonstandard counterpart. The solution of the linear quadratic Gaussian optimal control problem is obtained by solving the pure-slow and pure-fast reduced-order continuous-time algebraic Riccati equations and by implementing the pure-slow and pure-fast reduced-order Kalman filters. In order to show the effectiveness of the proposed method, we present the numerical result for a one-link flexible robot arm.

scholarly journals Model Order Reduction for Stochastic Optimal Control

2012 ◽  
Author(s):  
Ngoc-Hien Nguyen ◽  
Karen Willcox ◽  
Boo Cheong Khoo
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Real Time ◽  
Stochastic Optimal Control ◽  
Reduced Order Model ◽  
Full Model ◽  
Order Model ◽  
Reduced Order ◽  
Flow Quality

This work presents an approach to solve stochastic optimal control problems in the application of flow quality management in reservoir systems. These applications are challenging because they require real-time decision-making in the presence of uncertainties such as wind velocity. These uncertainties must be accounted for as stochastic variables in the mathematical model. In addition, computational costs and storage requirements increase rapidly due to the stochastic nature of the simulations and optimisation formulations. To overcome these challenges, an approach is developed that uses the combination of a reduced-order model and an adjoint-based method to compute the optimal solution rapidly. The system is modelled by a system of stochastic partial differential equations. The finite element method together with collocation in the stochastic space provide an approximate numerical solution—the “full model”, which cannot be solved in real-time. The proper orthogonal decomposition and Galerkin projection technique are applied to obtain a reduced-order model that approximates the full model. The conjugate-gradient method with Armijo line-search is then employed to find the solution of the optimal control problem under the uncertainty of input parameters. Numerical results show that the stochastic control yields solutions that are above the bound of the set solutions of the deterministic control. Applying the reduced model to the stochastic optimal control problem yields a speed-up in computational time by a factor of about 80 with acceptable accuracy in comparison with the full model. Application of the optimal control strategy shows the potential effectiveness of this computational modeling approach for managing flow quality.

scholarly journals POD-Galerkin Model Order Reduction for Parametrized Nonlinear Time Dependent Optimal Flow Control: an Application to Shallow Water Equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Maria Strazzullo ◽  
Francesco Ballarin ◽  
Gianluigi Rozza
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Control Problems ◽  
Order Reduction ◽  
Time Dependent ◽  
Shallow Waters ◽  
Control Problems ◽  
Reduced Order ◽  
Low Dimensional

Abstract In this work we propose reduced order methods as a reliable strategy to efficiently solve parametrized optimal control problems governed by Shallow Waters Equations in a solution tracking setting. The physical parametrized model we deal with is nonlinear and time dependent: this leads to very time consuming simulations which can be unbearable e.g. in a marine environmental monitoring plan application. Our aim is to show how reduced order modelling could help in studying different configurations and phenomena in a fast way. After building the optimality system, we rely on a POD-Galerkin reduction in order to solve the optimal control problem in a low dimensional reduced space. The presented theoretical framework is actually suited to general nonlinear time dependent optimal control problems. The proposed methodology is finally tested with a numerical experiment: the reduced optimal control problem governed by Shallow Waters Equations reproduces the desired velocity and height profiles faster than the standard model, still remaining accurate.

Control of a biped locomotion system in a double support phase

Robotica ◽  
1985 ◽  
Vol 3 (2) ◽  
pp. 73-77 ◽  
Author(s):  
Tatsuo Narikiyo ◽  
Masami Ito
Keyword(s):  
Control Problem ◽  
Control Algorithm ◽  
Biped Locomotion ◽  
Reduced Order ◽  
Double Support ◽  
Locomotion System ◽  
Constrained Equations ◽  
Reduced Space ◽  
Support Phase ◽  
Double Support Phase

This paper considers theoretically and experimentally the control problem of the biped locomotion system on the double support phase. The motion on the double support phase is described by the constrained dynamic system with two static constraints. The reduced order equations are derived by eliminating Lagrange's multiplier from the constrained equations, and a control algorithm for stabilizing the motion is obtained in reduced space. Finally, this algorithm is applied to an actual robot constructed in our laboratory and its usefulness is shown.

scholarly journals Reduced Order Solution of Nonstandard H^|^infin; Control Problem

1996 ◽  
Vol 32 (1) ◽  
pp. 16-25 ◽  
Author(s):  
Takao WATANABE ◽  
Keiichiro YASUDA ◽  
Ryuichi YOKOYAMA
Keyword(s):  
Control Problem ◽  
Reduced Order ◽  
Order Solution
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